Cambridge Additional Mathematics

264 Counting and the binomial expansion (Chapter 10)

Example 11 Self Tutor

The alphabet blocks A, B, C, D, and E are placed in a row in front of you.

a How many different permutations could you have?

b How many permutations end in C?

c How many permutations have the form

d How many begin and end with a vowel (A or E)?

a There are 5 letters taken 5 at a time.

) the total number of permutations=5£ 4 £ 3 £ 2 £1 = 5! = 120.

b C must be in the last position. The other 4 letters could go into

the remaining 4 places in4!ways.

) the number of permutations=1£4! = 24.

c A goes into 1 place. B goes into 1 place. The remaining 3 letters

go into the remaining 3 places in3!ways.

) the number of permutations=1£ 1 £3! = 6.

d A or E could go into the 1 st position, so there are two options.

The other one must go into the last position.

The remaining 3 letters could go into the 3 remaining places in

3!ways.

) the number of permutations=2£ 1 £3! = 12.

EXERCISE 10D

1 List the set of all permutations on the symbols W, X, Y, and Z taken:

a 1 at a time b two at a time c three at a time.

2 List the set of all permutations on the symbols A, B, C, D, and E taken:

a 2 at a time b 3 at a time.

3 In how many ways can:

a 5 different books be arranged on a shelf

b 3 different paintings be chosen from a collection of 8 , and hung in a row

c a signal consisting of 4 coloured flags in a row be made if there are 10 different flags to choose

from?

4 A captain and vice-captain are to be selected from a team of 11 cricketers. In how many ways can this

be done?

5 Suppose you have 4 different coloured flags. How many different signals could you make using:

a 2 flags in a row b 3 flags in a row c 2 or 3 flags in a row?

6 Nine boxes are each labelled with a different whole number from 1 to 9. Five people are allowed to

take one box each. In how many different ways can this be done if:

a there are no restrictions

b the first three people decide that they will take even numbered boxes?

any others

here

C here

4 3 211

A

3 1 2 1 1

B

AorE remainder

of A or E

2 3 211

...A... B ...?

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_10\264CamAdd_10.cdr Monday, 23 December 2013 4:29:53 PM BRIAN